Abstract
In the present paper, a novel approach to parallel computations for solving time-consuming multicriteria global optimization problems is presented. This approach includes various methods for the scalarization of vector criteria, dimensionality reduction with the use of the Peano space-filling curves, and efficient global search algorithms. The applied criteria scalarization methods can be altered in the course of computations in order to better meet the stated optimality requirements. To reduce the computational complexity of multicriteria problems, the methods developed feature an extensive use of all the computed optimization information and are well parallelized for effective performance on high-performance computing systems. Numerical experiments confirmed the efficiency of the developed approach.
This research was supported by the Russian Science Foundation, project No. 16-11-10150 “Novel efficient methods and software tools for time-consuming decision making problems using supercomputers of superior performance.”.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Marler, R.T., Arora, J.S.: Multi-Objective Optimization: Concepts and Methods for Engineering. VDM Verlag, Saarbrücken (2009)
Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2010). https://doi.org/10.1007/3-540-27659-9
Collette, Y., Siarry, P.: Multiobjective Optimization: Principles and Case Studies. Decision Engineering. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-662-08883-8
Pardalos, P.M., Žilinskas, A., Žilinskas, J.: Non-Convex Multi-Objective Optimization. Springer Optimization and Its Applications, vol. 123. Springer, Cham (2017)
Modorskii, V.Y., Gaynutdinova, D.F., Gergel, V.P., Barkalov, K.A.: Optimization in design of scientific products for purposes of cavitation problems. In: AIP Conference Proceedings, vol. 1738, p. 400013 (2016). https://doi.org/10.1063/1.4952201
Gergel, V.P., Strongin, R.G.: Parallel computing for globally optimal decision making. In: Malyshkin, V.E. (ed.) PaCT 2003. LNCS, vol. 2763, pp. 76–88. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45145-7_7
Gergel, V., Kozinov, E.: Efficient methods of multicriterial optimization based on the intensive use of search information. In: Kalyagin, V.A., Nikolaev, A.I., Pardalos, P.M., Prokopyev, O.A. (eds.) NET 2016. SPMS, vol. 197, pp. 27–45. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56829-4_3
Barkalov, K., Gergel, V., Lebedev, I.: Solving global optimization problems on GPU cluster. In: AIP Conference Proceedings, vol. 1738, p. 400006 (2016)
Gergel, V., Kozinov, E.: Efficient multicriterial optimization based on intensive reuse of search information. J. Global Optim. 71(1), 73–90 (2018). https://doi.org/10.1007/s10898-018-0624-3
Strongin, R., Sergeyev, Ya.: Global Optimization with Non-Convex Constraints. Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2nd edn. 2013, 3rd edn. 2014)
Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. SpringerBriefs in Optimization. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-8042-6
Zhigljavsky, A., Žilinskas, A.: Stochastic Global Optimization. Springer Optimization and Its Applications. Springer, New York (2008). https://doi.org/10.1007/978-0-387-74740-8
Locatelli, M., Schoen, F.: Global Optimization: Theory, Algorithms, and Applications. SIAM, Philadelphia (2013)
Floudas, C.A., Pardalos, M.P.: Recent Advances in Global Optimization. Princeton University Press, Princeton (2016)
Gergel, V., Sidorov, S.: A two-level parallel global search algorithm for solution of computationally intensive multiextremal optimization problems. In: Malyshkin, V. (ed.) PaCT 2015. LNCS, vol. 9251, pp. 505–515. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21909-7_49
Gergel, V., Kozinov, E.: Parallel computing for time-consuming multicriterial optimization problems. In: Malyshkin, V. (ed.) PaCT 2017. LNCS, vol. 10421, pp. 446–458. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62932-2_43
Sergeyev, Y.D., Kvasov, D.E.: A deterministic global optimization using smooth diagonal auxiliary functions. Commun. Nonlinear Sci. Numer. Simul. 21(1–3), 99–111 (2015)
Gergel, V., Grishagin, V., Gergel, A.: Adaptive nested optimization scheme for multidimensional global search. J. Global Optim. 66(1), 35–51 (2015). https://doi.org/10.1007/s10898-015-0355-7
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Gergel, V., Kozinov, E. (2020). Parallel Computations for Various Scalarization Schemes in Multicriteria Optimization Problems. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12043. Springer, Cham. https://doi.org/10.1007/978-3-030-43229-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-43229-4_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-43228-7
Online ISBN: 978-3-030-43229-4
eBook Packages: Computer ScienceComputer Science (R0)